Subject: Factor Theorem
Who is asking: Student Level: Secondary
Question: Hi, I'm not sure what to do with this question:
Prove (x - a - b) is a factor of x3 - a3 - b3 - 3ab (a + b)
I don't know even how to start it!
The integer 3 is a factor of 414. I know this because, if I divide 414 by 3 the remainder is zero. You could apply the same argument here. Divide x3 - a3 - b3 - 3ab (a + b) by (x -a -b) and show that the remainder is zero. Fortunately there is another procedure you can apply.
The factor theorem states that
f(a + b) = (a + b)3 - a3 - b3 - 3ab (a + b)
Expand (a + b)3 and show that f(a + b) = 0.Penny
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